Weak Scatterers Research Articles

Statistical classification of weak backscattering scatterers of PolSAR image

Statistical classification of weak backscattering scatterers of PolSAR image

Lab Source Anomalous Scattering Using Cr Kα Radiation

High-throughput crystallography requires a method by which the structures of proteins can be determined quickly and easily. Experimental phasing is an essential technique in determining the three-dimensional protein structures using single-crystal X-ray diffraction. In macromolecular crystallography, the phases are derived either by Molecular Replacement (MR) method using the atomic coordinates of a structurally similar protein or by locating the positions of heavy atoms that are intrinsic to the protein or that have been added (MIR, MIRAS, SIR, SIRAS, MAD and SAD). Availability of in-house lab data collection sources (Cu Kα and Cr Kα radiation), cryo-crystallography and improved software for heavy atom location and density modification have increased the ability to solve protein structures using SAD. SAD phasing using intrinsic anomalous scatterers like sulfur, chlorine, calcium, manganese and zinc, which are already present in the protein becomes increasingly attractive owing to the advanced phasing methods. An analysis of successful SAD phasing on three proteins, lysozyme, glucose isomerase and thermolysin based on the signal of weak anomalous scatterers such as sulfur atom and chloride ion have been carried out. This analysis also proves that even the anomalous signal provided or present naturally in a macromolecule is good enough to solve crystal structures successfully using lab source chromium-generated X-ray radiation.

Cramér-Rao Bound Study of Multiple Scattering Effects in Target Separation Estimation

The information about the distance of separation between two-point targets that is contained in scattering data is explored in the context of the scalar Helmholtz operator via the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased target separation estimation. The CRB results are obtained for the exact multiple scattering model and, for reference, also for the single scattering or Born approximation model applicable to weak scatterers. The effects of the sensing configuration and the scattering parameters in target separation estimation are analyzed. Conditions under which the targets' separation cannot be estimated are discussed for both models. Conditions for multiple scattering to be useful or detrimental to target separation estimation are discussed and illustrated.

Coherent Random Fiber Laser Based on Nanoparticles Scattering in the Extremely Weakly Scattering Regime

We demonstrate the realization of a coherent random fiber laser (RFL) in the extremely weakly scattering regime, which contains a dispersive solution of polyhedral oligomeric silsesquioxanes nanoparticles (NPs) and laser dye pyrromethene 597 in carbon disulfide that was injected into a hollow optical fiber. Multiple scattering of polyhedral oligomeric silsesquioxanes NPs greatly enhanced by the waveguide confinement effect was experimentally verified to account for coherent lasing observed in our RFL system. This Letter extends the NPs-based RFLs from the incoherent regime to the coherent regime.

Green function solution of a second-order partial differential equation and conductivity of thin films

Correct form of the Green function G of the Schrödinger equation is developed for a thin metallic film of thickness d which contains infinitesimally weak volume and surface scatterers. Conductivity σ of the film is obtained from the imaginary part of the self-energy Σ appearing in the average G and increases smoothly with d and that density of states is not staircaselike as contrast to the usual. Examination of σ in terms of d agrees well with the experiment.

Single Realization Stochastic FDTD for Weak Scattering Waves in Biological Random Media

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result.

Optimization-Based Terahertz Imaging

A terahertz (THz) imaging modality based on nonlinear optimization that is not limited by weak scatter or low refractive index is presented. Two-dimensional reconstructions of sub-wavelength dielectric cylinders in air are performed through iterative coordinate descent (ICD) optimization in a Bayesian framework using experimental data obtained by illuminating the objects with a THz beam. Strategies for avoiding local minima and to allow for faster convergence and improved image quality are presented and evaluated.

An Improved Space Debris ISAR Imaging Algorithm

According to the Characteristics of space debris, single-range matching filtering (SRMF) can be used for space debris inverse synthetic aperture radar (ISAR) imaging. Combined SRMF and Coherent CLEAN algorithm can effectively solve high sidelobes problem brought by Fourier transform. However, when the SNR is low, the position error of scattering centers extracted by SRMF-CLEAN is big, and even some weak scatterings can’t be extracted. This paper uses Sequence CLEAN instead of Coherent CLEAN to availably solve the above problems. The experiment results confirm the validness of the proposed algorithm.

Wave shadowing and modulation of microwave backscatter from the ocean

Shadowing and modulation of microwave backscatter by ocean waves are studied using coherent X‐band radars. Two types of shadowing are investigated: geometric shadowing (complete blockage of incident rays) and partial shadowing (polarization‐dependent diffraction combined with weak scatterers). We point out that the frequency of occurrence of zero signal‐to‐noise ratio samples cannot depend on the incident power level or the polarization if geometric shadowing occurs but can if partial shadowing exists. We then compare this behavior with observations, and show that the data do not support the hypothesis that geometric shadowing plays a significant role in low‐grazing‐angle microwave scattering from the ocean surface. Furthermore, our data indicate that partial shadowing only depends significantly on polarization for the steep waves found near shorelines. We also study the modulation of microwave backscatter by ocean waves using these data by looking at the phase differences between received power and scatterer velocity. These phase differences appear to be rather well explained by standard composite surface theory at VV polarization, having values that are positive looking up wave and negative looking down wave. For HH polarization, however, breaking effects come into play and overshadow composite surface effects of free waves. They cause the phase difference to be near zero for up wave looks and near 180° for down‐wave looks. A simple model that involves both breaking and freely propagating waves but does not include any shadowing effects is shown to account for observed phase differences at both polarizations to within about 10°.

The effect of phase scintillations on the accuracy of phase screen simulation using deterministic screens derived from GPS and ALTAIR measurements

Radio receivers capable of high‐rate sampling such as GPS scintillation monitors and the ALTAIR VHF/UHF tracking radar can measure ionospheric phase fluctuations suitable for scintillation modeling using phase screen techniques. For modeling purposes, the phase variations caused by the refractive effects of electron density irregularities encountered along the propagation path are desired. The phase fluctuations measured by ground‐based receivers, however, also include the unwanted effects of diffraction (phase scintillations). In this paper, we investigate the effect of phase scintillations on the accuracy of phase screen simulation when using the phase measured on the ground as a proxy for the ionospheric screen. Using stochastic and deterministic (measured) phase screens, we quantitatively assess the accuracy of this approach by cross‐correlating the predicted and measured intensity fluctuations. We find that the intensity cross‐correlation is less than unity even in the weak scatter limit, due to the presence of weak phase scintillations. This correlation decreases rapidly with increasing irregularity strength once rapid transitions in the phase (strong phase scintillations) develop. We demonstrate that, when using the measured phase on the ground as a proxy for the ionospheric screen, both the temporal structure of simulated fluctuations and their statistics deviate increasingly from those of the measurements as the turbulence strength increases, especially when strong phase scintillations are present. We also demonstrate that back‐propagating the complex signal up to ionospheric altitudes prior to the forward propagation calculation yields improved results, but some errors still remain as a consequence of neglecting amplitude fluctuations which develop inside the random medium.

3D Localization of weak scatterers in digital holographic microscopy using Rayleigh-Sommerfeld back-propagation

The Rayleigh-Sommerfeld back-propagation method is a fast and highly flexible volume reconstruction scheme for digital holographic microscopy. We present a new method for 3D localization of weakly scattering objects using this technique. A well-known aspect of classical optics (the Gouy phase shift) can be used to discriminate between objects lying on either side of the holographic image plane. This results in an unambiguous, model-free measurement of the axial coordinate of microscopic samples, and is demonstrated both on an individual colloidal sphere, and on a more complex object — a layer of such particles in close contact.

WIMP diffusion in the Solar System including solar WIMP-nucleon scattering

Dark matter in the form of Weakly Interacting Massive Particles (WIMPs) can be captured by the Sun and the Earth, sink to their cores, annihilate and produce neutrinos that can be searched for with neutrino telescopes. The calculation of the capture rates of WIMPs in the Sun and especially the Earth are affected by large uncertainties coming mainly from effects of the planets in the Solar System, reducing the capture rates by up to an order of magnitude (or even more in some cases). We show that the WIMPs captured by weak scatterings in the Sun also constitute an important bound WIMP population in the Solar System. Taking this population and its interplay with the population bound through gravitational diffusion into account cancel the planetary effects on the capture rates, and the capture essentially proceeds as if the Sun and the Earth were free in the galactic halo. The neutrino signals from the Sun and the Earth are thus significantly higher than claimed in the scenarios with reduced capture rates.

Microwave Imaging Within the First-Order Born Approximation by Means of the Contrast-Field Bayesian Compressive Sensing

A new approach based the contrast field (CF) formulation of the microwave imaging problem that exploits the Bayesian compressive sampling (BCS) paradigm is proposed for the reconstruction of sparse distributions of weak scatterers. Towards this end, the original inverse scattering problem is recast to a probabilistic sparseness constrained optimization by introducing suitable hierarchical priors as sparsity constraints. A fast relevance vector machine (RVM) is then employed to reconstruct the scatterers as well as to estimate the “confidence level” of the inversion. Representative numerical results are presented to illustrate the method as well as to assess its potentialities and limitations in terms of inversion accuracy, computational efficiency, and robustness. Comparisons with state-of-the-art deterministic and stochastic reconstruction methodologies still within the Born approximation (BA) are discussed, as well.

Propagation of guided waves through weak penetrable scatterers

The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed.

Cramér-Rao Bound Study of Multiple Scattering Effects in Target Localization

The target position information contained in scattering data is explored in the context of the scalar Helmholtz operator for the basic two-point scatterer system by means of the statistical estimation framework of the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased position estimation. The CRB results are derived for the exact multiple scattering model and, for reference, also for the single scattering or first Born approximation model applicable to weak scatterers. The roles of the sensing configuration and the scattering parameters in target localization are analyzed. Blind spot conditions under which target localization is impossible are derived and discussed for both models. It is shown that the sets of sensing configuration and scattering parameters for which localization is impeded are different but equivalent (they have the same size) under the exact multiple scattering model and the Born approximation. Conditions for multiple scattering to be useful or detrimental to localization are derived.

Two routes to magnetic order by disorder in underdoped cuprates

We study disorder-induced magnetism within the Gutzwiller approximation applied to the t-J model relevant for cuprate superconductors. In particular, we show how disorder generates magnetic phases by inducing local droplets of antiferromagnetic order which eventually merge, and form a quasi-long range ordered state in the underdoped regime. We identify two distinct disorder-induced magnetic phases of this type depending on the strength of the scatterers. For weak potential scatterers used to model dopant disorder, charge reorganization may push local regions in-between the impurities across the magnetic phase boundary, whereas for strong scatterers used to model substitutional ions, a local static magnetic moment is formed around each impurity. We calculate the density of states and find a remarkably universal low-energy behavior largely independent of both disorder and magnetization. However, the magnetic regions are characterized by larger (reduced) superconducting gap (coherence peaks) and a sub-gap kink in the density of states.

ANODE: anomalous and heavy-atom density calculation

The new program ANODE estimates anomalous or heavy-atom density by reversing the usual procedure for experimental phase determination by methods such as single- and multiple-wavelength anomalous diffraction and single isomorphous replacement anomalous scattering. Instead of adding a phase shift to the heavy-atom phases to obtain a starting value for the native protein phase, this phase shift is subtracted from the native phase to obtain the heavy-atom substructure phase. The required native phase is calculated from the information in a Protein Data Bank file of the structure. The resulting density enables even very weak anomalous scatterers such as sulfur to be located. Potential applications include the identification of unknown atoms and the validation of molecular replacement solutions.

On QM/MM and MO/MO cluster calculations of all-atom anisotropic displacement parameters for molecules in crystal structures

The practical aspects of ab initio calculation of anisotropic displacement parameters (ADPs) for molecules in crystal structures are investigated. Computationally efficient approaches to calculate ADPs are QM/MM or MO/MO methods, where quantum chemical calculations are split into a high-level and a low-level part. Such calculations allow geometry optimizations and subsequent frequency calculations of a central molecule in a cluster of surrounding molecules as found in the crystal lattice. The frequencies and associated displacements are then converted into ADPs. A series of such calculations were performed with different quantum chemical methods and basis sets on the three zwitterionic amino-acid structures of L-alanine, L-cysteine and L-threonine, where high-quality low-temperature X-ray data are available. To scale and compare calculated ADPs, X-ray ADPs from invariom refinement were used. The future use of calculated ADPs will include the investigation of systematic errors in experimental X-ray diffraction data. Completion of an isotropic structural model is already possible. Calculated ADPs might also make it possible to perform charge-density studies on data sets of limited resolution/coverage as obtained from weak scatterers, high-pressure measurements or to deconvolute electron density obtained from the maximum-entropy method.

Physics of a rapid CD4 lymphocyte count with colloidal gold

The inherent surface charges and small diameters that confer colloidal stability to gold particle conjugates (immunogold) are detrimental to rapid cell surface labeling and distinct cluster definition in flow cytometric light scatter assays. Although the inherent immunogold surface charge prevents self aggregation when stored in liquid suspension, it also slows binding to cells to timeframes of hours and inhibits cell surface coverage. Although the small diameter of immunogold particles prevents settling when in liquid suspension, small particles have small light scattering cross sections and weak light scatter signals. We report a new, small particle lyophilized immunogold reagent that maintains activity after 42°C storage for a year and can be rapidly dissolved into stable liquid suspension for use in labelling cells with larger particle aggregates that have enhanced scattering cross section. Labeling requires less than 1 min at 20°C, which is ∼30 times faster than customary fluorescent antibody labeling. The labeling step involves neutralizing the surface charge of immunogold and creating specifically bound aggregates of gold on the cell surface. This process provides distinct side-scatter cluster separation with blue laser light at 488 nm, which is further improved by using red laser light at 640 nm. Similar comparisons using LED light sources showed less improvement with red light, thereby indicating that coherent light scatter is of significance in enhancing side-scatter cluster separation. The physical principles elucidated here for this technique are compatible with most flow cytometers; however, future studies of its clinical efficacy should be of primary interest in point-of-care applications where robust reagents and rapid results are important.

Effects of cell spatial organization and size distribution on ultrasound backscattering

In ultrasound tissue characterization dealing with cellular aggregates (such as tumors), it can be hypothesized that cell microstructure and spatial distribution dominate the backscatter signal. Effects of spatial organization and size distribution of nuclei in cell aggregates on ultrasound backscatter are examined in this work using 2-D computer simulations. The nuclei embedded in cytoplasm were assumed to be weak scatterers of incident ultrasound waves, and therefore multiple scattering could be neglected. The fluid sphere model was employed to obtain the scattering amplitude for each nucleus and the backscatter echo was generated by summing scattered signals originating from many nuclei. A Monte Carlo algorithm was implemented to generate realizations of cell aggregates. It was found that the integrated backscattering coefficient (IBSC) computed between 10 and 30 MHz increased by about 27 dB for a spatially random distribution of mono-disperse nuclei (radius = 4.5 μm) compared with that of a sample of periodically positioned mono-disperse nuclei. The IBSC also increased by nearly 7 dB (between 10 and 30 MHz) for a spatially random distribution of poly-disperse nuclei (mean radius ± SD = 4.5 ± 1.54 μm) compared with that of a spatially random distribution of mono-disperse nuclei. Two different Gaussian pulses with center frequencies 5 and 25 MHz were employed to study the backscatter envelope statistics. An 80% bandwidth was chosen for each case with approximately 0.32 mm as the full-width at half-maximum (FWHM) for the first pulse and 0.06 mm for the second. The incident beam was approximated as a Gaussian beam (FWHM = 2.11 and 1.05 mm for those pulses, respectively). The backscatter signal envelope histograms generally followed the Rayleigh distribution for mono-disperse and poly-disperse samples. However, for samples with partially ordered nuclei, if the irradiating pulse contained a frequency for which ultrasound wavelength and scatter periodicity became comparable (d ~ λ/2), then the histograms were better fitted by the Nakagami distribution. This study suggests that the shape of an envelope histogram depends upon the periodicity in the spatial organization of scatterers and bandwidth of the ultrasound pulse.